Emergent Complexity in Conway’s Game of Life

  • Nick GottsEmail author


It is shown that both small, finite patterns and random infinite very low density (“sparse”) arrays of the Game of Life can produce emergent structures and processes of great complexity, through ramifying feedback networks and cross-scale interactions. The implications are discussed: it is proposed that analogous networks and interactions may have been precursors to natural selection in the real world.


Cellular Automaton Quadratic Growth Growth Cluster Global Density Feedback Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Axtell, R.: U.S. firm sizes are Zipf distributed. Science 293, 1818–1820 (2001) CrossRefGoogle Scholar
  2. 2.
    Bak, P., Chen, K., Creutz, M.: Self-organized criticality in the “Game of Life”. Nature 342, 780–781 (1989) CrossRefGoogle Scholar
  3. 3.
    Barabási, A.-L.: Linked: The New Science of Networks. Perseus, Cambridge (2002) Google Scholar
  4. 4.
    Barrow, J.D., Tipler, F.J.: The Anthropic Cosmological Principle. Oxford University Press, Oxford (1986) Google Scholar
  5. 5.
    Bell, D.I.: Highlife: an interesting variant of Life. Available from (1994)
  6. 6.
    Berlekamp, E., Conway, J.H., Guy, R.: Winning Ways, vol. 2. Academic Press, San Diego (1982) zbMATHGoogle Scholar
  7. 7.
    Braga, G., Catteneo, G., Flocchini, P., Quaranta Vogliotti, Q.: Pattern growth in elementary cellular automata. Theor. Comput. Sci. 145, 1–26 (1995) zbMATHCrossRefGoogle Scholar
  8. 8.
    Carroll, G.R.: National city-size distributions. Prog. Hum. Geogr. 6, 1–43 (1982) CrossRefGoogle Scholar
  9. 9.
    Casti, J.L.: Would-Be Worlds: How Simulation Is Changing the Frontiers of Science. Wiley, New York (1997) Google Scholar
  10. 10.
    Chang, T., Tam, S.W.Y., Wu, C.-C., Consolini, G.: Complexity, forced and/or self-organised criticality, and topological phase transitions in space plasmas. Space Sci. Rev. 107, 425–445 (2003) CrossRefGoogle Scholar
  11. 11.
    Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004) zbMATHGoogle Scholar
  12. 12.
    Dhar, A., Lakdawala, P., Mandal, G.: Role of initial conditions in the classification of the rule-space of cellular-automata dynamics. Phys. Rev. E 51(4, Pt. A), 3032–3037 (1995) CrossRefGoogle Scholar
  13. 13.
    Fleck, J.: Artefact activity: the coevolution of artefacts, knowledge and organization in technological innovation. In: Ziman, J. (ed.) Technological Innovation as an Evolutionary Process, pp. 248–266. Cambridge University Press, Cambridge (2000) Google Scholar
  14. 14.
    Fu, L.-L.: Interaction of mesoscale variability with large-scale waves in the Argentine basin. J. Phys. Oceanogr. 37, 787–797 (2007) CrossRefGoogle Scholar
  15. 15.
    Gardner, M.: Wheels, Life and Other Mathematical Amusements. Freeman, New York (1983) zbMATHGoogle Scholar
  16. 16.
    Gönerup, O., Crutchfield, J.P.: Hierarchical self-organization in the finitary process soup. Santa Fe Institute working paper 06-03-008 (2006) Google Scholar
  17. 17.
    Gotts, N.M.: Emergent phenomena in large sparse random arrays of Conway’s “Game of Life”. Int. J. Syst. Sci. 31(7), 873–894 (2000) zbMATHCrossRefGoogle Scholar
  18. 18.
    Gotts, N.M.: Self-organised construction in sparse random arrays of Conway’s Game of Life. In: Griffeath, D., Moore, C. (eds.) New Constructions in Cellular Automata. Santa Fe Institute. Studies in the Sciences of Complexity, pp. 1–53. Oxford University Press, Oxford (2003) Google Scholar
  19. 19.
    Gotts, N.M.: Ramifying feedback networks, cross-scale interactions, and emergent quasi individuals in Conway’s Game of Life. Artif. Life 15(3), 351–375 (2009) CrossRefGoogle Scholar
  20. 20.
    Gotts, N.M., Callahan, P.B.: Emergent structures in sparse fields of Conway’s “Game of Life”. In: Adami, C., Belew, R.K., Kitano, H., Taylor, C. (eds.) Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life, pp. 104–113. MIT, Cambridge (1998) Google Scholar
  21. 21.
    Hanson, J.E., Crutchfield, J.P.: Computational mechanics of cellular automata: an example. Physica D 103(1–4), 169–189 (1997) CrossRefMathSciNetGoogle Scholar
  22. 22.
    Holling, C.S., Peterson, F., Marples, P., Sendzimir, J., Redford, K., Gunderson, L., Lambert, D.: Self-organization in ecosystems: lumpy geometries, periodicities and morphologies. In: Walker, B.H., Steffen, W.L. (eds.) Global Change and Terrestrial Ecosystems, pp. 346–384. Cambridge University Press, Cambridge (1996) Google Scholar
  23. 23.
    Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford University Press, Oxford (1993) Google Scholar
  24. 24.
    Koonin, E.V., Martin, W.: On the origin of genomes and cells within inorganic compartments. Trends Genet. 21, 649–654 (2005) CrossRefGoogle Scholar
  25. 25.
    Langton, C.G.: Self-reproduction in cellular automata. Physica D 10, 134–144 (1984) CrossRefGoogle Scholar
  26. 26.
    Martin, W., Russell, M.J.: On the origins of cells: a hypothesis for the evolutionary transitions from abiotic geochemistry to chemoautotrophic prokaryotes, and from prokaryotes to nucleated cells. Philos. Trans. R. Soc. Lond. A: Biol. Sci. 358, 59–85 (2002) CrossRefGoogle Scholar
  27. 27.
    Maynard Smith, J., Szathmáry, E.: The Major Transitions in Evolution. Freeman, New York (1995) Google Scholar
  28. 28.
    Pargellis, A.N.: The evolution of self-replicating computer organisms. Physica D 98, 111–127 (1996) zbMATHCrossRefGoogle Scholar
  29. 29.
    Peters, D.P.C., Pielke, R.A. Sr., Bestelmeyer, B.T., Allen, C.D., Munson-McGee, S., Havstad, K.M.: Cross-scale interactions, nonlinearities, and forecasting catastrophic events. Proc. Natl. Acad. Sci. USA 101(42), 15130–15135 (2004). www.pnas.org_cgi_doi_10.1073_pnas.0403822101 CrossRefGoogle Scholar
  30. 30.
    Peterson, G.D., Allen, C.R., Holling, C.S.: Ecological resilience, biodiversity and scale. Ecosyst. 1, 6–18 (1998) CrossRefGoogle Scholar
  31. 31.
    Poundstone, W.: The Recursive Universe. Morrow, New York (1985) Google Scholar
  32. 32.
    Shante, V.K.S., Kirkpatrick S.: An introduction to percolation theory. Adv. Phys. 20, 325–357 (1971) CrossRefGoogle Scholar
  33. 33.
    Silver, S.: Personal communication (1998) Google Scholar
  34. 34.
    Simon, H.A.: The Sciences of the Artificial, 3rd edn. MIT, Cambridge (1996) Google Scholar
  35. 35.
    Theraulaz, G., Bonabeau, E.: A brief history of stigmergy. Artif. Life 5(2), 97–116 (1999) CrossRefGoogle Scholar
  36. 36.
    Tjardes, T., Neugebauer, E.: Sepsis research in the next millennium: concentrate on the software rather than the hardware. Shock 17(1), 1–8 (2002) CrossRefGoogle Scholar
  37. 37.
    von Neumann, J.: The Theory of Self-reproducing Automata. University of Illinois, Urbana (1966) Google Scholar
  38. 38.
    Winfree, A.T.: When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton University Press, Princeton (1987) Google Scholar
  39. 39.
    Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984) CrossRefMathSciNetGoogle Scholar

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© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Integrated Land Use SystemsMacaulay Land Use Research InstituteAberdeenUK

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